The equation of a circle $C$ is $(x+2)^{2}+(y-7)^{2} = 49$. What are its center $(h, k)$ and its radius $r$ ?
Solution: The equation of a circle with center $(h, k)$ and radius $r$ is $(x - h)^2 + (y - k)^2 = r^2$ We can rewrite the given equation as $(x - (-2))^2 + (y - 7)^2 = 7^2$ Thus, $(h, k) = (-2, 7)$ and $r = 7$.